Kohler had three ignition systems on the early K series, Two of which were electronic (breaker-less). What you need to do is identify which system you have on this unit.
Jumping battery voltage to either of these breaker-less systems could result in fried components.
You can down-load a service manual below by clicking "Enter as Guest" then follow the prompts. Go to section 8 which will identify these systems and supply proper testing procedures.